On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/60267DOI: 10.1007/s00208-023-02780-x
ISSN: 0025-5831
Publisher
Springer
Date
2023-12-25Embargo end date
2024-12-25Funders
Agencia Estatal de Investigación
Universidad de Alcalá
Bibliographic citation
Lastra Sedano, A. & Malek, S. 2023, “On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations”, Mathematische Annalen, pp. 1-48.
Keywords
q-Gevrey asymptotic expansions
Monodromy
logarithmic type solutions
Singularly perturbed
Formal solution
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105621GB-I00/ES/METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOS/
info:eu-repo/grantAgreement/UAH//CM-JIN-2021-014
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica, Técnica y de Innovación 2021-2023/TED2021-129813A-I00
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1007/s00208-023-02780-xRights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2023 The Authors, under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature
Access rights
info:eu-repo/semantics/embargoedAccess
Abstract
A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-Gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.
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